We note in passing that the breakdown of a discrete symmetry during EWPT in the early universe can potentially lead to the problematic
EW-scale cosmic domain walls [1]} whose gravitational effects may
result in unacceptable anisotropy in the cosmic microwave background (CMB) radiation [2]}.
Depending on the stability and evolution of such domain walls, several mechanisms have been proposed to avoid these
quandaries [2]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}.
One of the mechanisms proposed in Refs. [2]}, [4]}, [5]}, [6]} was to assume that the discrete symmetry was not exact but approximate.
One can introduce a so-called “bias” term to the scalar potential to explicitly break the discrete symmetry. This term lifts the degenerate vacua and induces a difference
in the energy density between these vacua. This difference in the energy density has effects on the wall as a volume pressure and finally leads
to the decay of the wall when the pressure becomes comparable to the surface tension of the wall [14]}.
In a recent paper [15]}, the authors took our model and applied the approximate symmetry mechanism to solve the domain wall problem.
It was shown that there were two peaks in the GW spectrum, one from the first-order EWPT and the other from the domain wall decay.
